The Szilassi polyhedron is a heptahedron that is topologically equivalent to a torus and for which every
pair of faces has a polygon
edge in common. The Szilassi polyhedron has 14 polyhedron
vertices, seven faces, and 21 polyhedron
edges, and is the dual polyhedron of the Császár polyhedron. This polyhedron
was discovered by L. Szilassi in 1977. In the above illustration of the net,
sides indicated by letters are connected with the corresponding side indicated by
the same letter but with a different number of primes. Like the tetrahedron,
each face of the Szilassi polyhedron touches all other faces.
The skeleton of the Szilassi polyhedron is equivalent
to the Heawood graph, shown above.
